Simplify the expression and find an equivalent expression: \$ (3x^2 - 9xy + 6y^2)/(x^2 - 4xy + 4y^2) \$

A) \$ (x - y)/(x - 2y) \$

B) \$ (3(x - y))/(x - 2y) \$

C) \$ (3(x + y))/(3x + 2y) \$

D) \$ (3(x - 4y))/(x + 2y) \$

Solve the nonlinear equation:
\$sqrt(x+1) + root(3){x+1} = 2 \$

A) 1

B) 4

C) 0

D) \$ \sqrt3 \$

Show that the following system of equations has an infinite solution:
30x + 6y +18 = 0
4y + 10 = 22 + 20x

A) \$ (a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2) \$

B) \$ (a_1)/(a_2) ne (b_1)/(b_2) = (c_1)/(c_2) \$

C) \$ (a_1)/(a_2) ne (b_1)/(b_2) ne (c_1)/(c_2) \$

D) \$ (a_1)/(a_2) = (b_1)/(b_2) ne (c_1)/(c_2) \$

If there is no solution to the linear equation system
5y - kx = 10, 30x - 6y = 22, then find the value of k.

A) k = - 35

B) k = 60

C) k = - 30

D) k = 25

Solve the nonlinear equation:
\$ 2/(x-1) - 1/(x+2) = 1/x \$

A) \$ x = 3/2 \$

B) \$ x = 2 \$

C) \$ x = - 1/2 \$

D) \$ x = - 2/3 \$

Simplify the expression:
\$((4 x^3)-(16 x^2)+(12 x))/(2 x - 4)\$

A) \$(2 x^2)+ 4 x - 3 \$

B) \$(2 x^2)+ 2 x - 3 \$

C) \$(2 x^2) - 2 x + 3 \$

D) \$(2 x^2)+ 4 x + 3 \$

Simplify the expression if a = 3 and b = 2 :
\$((a^2 - 4ab + 4b^2)/(a - 2b)) times ((a + 2b) / (a^2 + 4ab + 4b^2))\$

A) \$ (7/8) \$

B) \$ - (1/7) \$

C) \$ (1/49) \$

D) \$ - (7/4) \$

Solve the nonlinear equation:
\$ w^2 - 5w + 6 = 0 \$

A) w = 2 and w = 3

B) w = 2 and w = 4

C) w = 5 and w = 3

D) w = 3 and w = 4

Determine the number of solutions for the following system of linear equations:
3x - 2y = 6
6x - 4y = 12

A) Unique solution

B) No solution

C) Not enough information

D) Infinitely many solutions

If the linear system 3x + 2y = 7 and 2 k x - 4y = 5 has no solution, find the value of k.

A) k = - 2

B) k = 3

C) k = - 3

D) k = 2